A loaded vertical spring executes simple harmonic oscillations with period of 4 s. The difference between the kinetic energy and potential energy of this system oscillates with a period of

Options

A. 8 s
B. 1 s
C. 2 s
D. 4 s

Answer

C

Explanation

`E_(k)-E_(P)=(1)/(2)momega^(2)[a^(2)-a^(2)sin^(2)omegat]+(1)/(2)momega^(2)a^(2)sin^(2)omegat`
`=(1//2)momega^(2)a^(2)[cos^(2)omegat-sin^(2)omegat]`
`E_(k)-E_(P)=(1//2)momega^(2)a^(2)cos2omegat`
`omega'=2omega therefore T'=(2pi)/(omega')=(2pi)/(2omega)=(pi)/(omega)`
The loaded spring have a period
`T=(2pi)/(omega)`
`(T')/(T)=(T)/(omega)xx(omega)/(2pi)=(1)/(2) therefore T'=(T)/(2)=(4)/(2)=2s`